Question

Suppose that we have two securities available for investment. Both of them have 50% to receive a payoff of 0, and 50% to receive a payoff of 2.

What is the expected payoff and what is the variance if we buy half a share of each? Answer this question for two cases: a) correlation between the stocks’ payoffs = -1; b) correlation = 1.

A. The expected payoff of the portfolio is 1 in a) and 0.5 in b), but the volatility stays the same (which is 1)

B. The expected payoff of the portfolio stays the same (which is 1), but the volatility of the portfolio is 0.5 in a) and 1 in b)

C. The expected payoff of the portfolio stays the same (which is 1), but the volatility of the portfolio is 0 in a) and 1 in b)

D. The expected payoff of the portfolio stays the same (which is 1), and the volatility of the portfolio is 1

Answer 1

Expected payoff = 50% * 0 + 50% *2 = 1

a)

Correlation between stocks = -1

As the correlation between A and B is -1, there is perfect negative correlation and the volatility will be zero

b)

As the correlation between stocks is 1, the volatility will be 1

Answer is C. The expected payoff of the portfolio stays the same (which is 1), but the volatility of the portfolio is 0 in a) and 1 in b)